Paper detail

The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling

While the existence of a spin-liquid ground state of the spin-1/2 kagome Heisenberg antiferromagnet (KHAF) is well established, the discussion of the effect of an interlayer coupling (ILC) by controlled theoretical approaches is still lacking. Here we study this problem by using the coupled-cluster method to high orders of approximation. We consider a stacked KHAF with a perpendicular ILC $J_\perp$, where we study ferro- as well as antiferromagnetic $J_\perp$. We find that the spin-liquid ground state (GS) persists until relatively large strengths of the ILC. Only if the strength of the ILC exceeds about 15\% of the intralayer coupling the spin-liquid phase gives way for $q=0$ magnetic long-range order, where the transition between both phases is continuous and the critical strength of the ILC, $|J^c_\perp|$, is almost independent of the sign of $J_\perp$. Thus, by contrast to the quantum GS selection of the strictly two-dimensional KHAF at large spin $s$, the ILC leads first to a selection of the $q=0$ GS. Only at larger $|J_\perp|$ the ILC drives a first-order transition to the $\sqrt{3}\times\sqrt{3}$ long-range ordered GS. As a result, the stacked spin-1/2 KHAF exhibits a rich GS phase diagram with two continuous and two discontinuous transitions driven by the ILC.